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Analog for the Wiener Lemma for Wolff-Denjoy SeriesAug 21 2019Let a function f with real poles be expanded in a Wolff-Denjoy series with positive coefficients. The main result of the note states that if we subtract its linear part from the function 1/f, then the remaining fractional part of this function will also ... More Constrained convex bodies with extremal affine surface areasAug 21 2019Given a convex body K in R^n and p in R, we introduce and study the extremal inner and outer affine surface areas IS_p(K) = sup_{K'\subseteq K} (as_p(K') ) and os_p(K)=inf_{K'\supseteq K} (as_p(K') ), where as_p(K') denotes the L_p-affine surface area ... More Complete boundedness of multiple operator integralsAug 21 2019In this paper, we characterize the multiple operator integrals mappings which are bounded on the Haagerup tensor product of spaces of compact operators. We show that such maps are automatically completely bounded and prove that this is equivalent to a ... More Quasi-local Algebras and Asymptotic ExpandersAug 21 2019In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a discrete metric space of bounded geometry. In the process, we introduce a weakening of the notion of expanders, called asymptotic ... More On the Banach lattice c_0Aug 21 2019We show that $c_0$ is not a projective Banach lattice, answering a question of B. de Pagter and A. Wickstead. On the other hand, we show that $c_0$ is complemented in the free Banach lattice generated by itself (seen as a Banach space). As a consequence, ... More Multilinear operator-valued Calderón-Zygmund theoryAug 20 2019We develop a general theory of multilinear singular integrals with operator-valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the $\mathcal R$-boundedness condition naturally arising ... More On coupled best proximity points and Ulam-Hyers stabilityAug 20 2019For two nonempty, closed, bounded and convex subsets $A$ and $B$ of a uniformly convex Banach space $X$ consider a mapping $T:(A \times B) \cup (B \times A) \rightarrow A \cup B$ satisfying $T(A,B) \subset B$ and $T(B, A) \subset A$. In this paper the ... More Operators which are polynomially isometric to a normal operatorAug 19 2019Aug 21 2019Let $\mathcal{H}$ be a complex, separable Hilbert space and $\mathcal{B}(\mathcal{H})$ denote the algebra of all bounded linear operators acting on $\mathcal{H}$. Given a unitarily-invariant norm $\| \cdot \|_u$ on $\mathcal{B}(\mathcal{H})$ and two linear ... More Normal operators with highly incompatible off-diagonal cornersAug 19 2019Let $\mathcal{H}$ be a complex, separable Hilbert space, and $\mathcal{B}(\mathcal{H})$ denote the set of all bounded linear operators on $\mathcal{H}$. Given an orthogonal projection $P \in \mathcal{B}(\mathcal{H})$ and an operator $D \in \mathcal{B}(\mathcal{H})$, ... More Dyadic norm Besov-type spaces as trace spaces on regular treesAug 19 2019In this paper, we study function spaces defined via dyadic energies on the boundaries of regular trees. We show that correct choices of dyadic energies result in Besov-type spaces that are trace spaces of (weighted) first order Sobolev spaces. On Two Families of Funk-Type TransformsAug 19 2019We consider two families of Funk-type transforms that assign to a function on the unit sphere the integrals of that function over spherical sections by planes of fixed dimension. Transforms of the first kind are generated by planes passing through a fixed ... More On the Hypercyclicity Criterion for operators of Read's typeAug 19 2019Let $T$ be a so-called operator of Read's type on a (real or complex) separable Banach space, having no non-trivial invariant subset. We prove in this note that $T\oplus T$ is then hypercyclic, i.e. that $T$ satisfies the Hypercyclicity Criterion. On the ${\Ext}^2$-problem for Hilbert spacesAug 18 2019We show that $\Ext^2(\ell_2, \ell_2)\neq 0$ in the category of Banach spaces. This solves a sharpened version of Palamodov's problem and provides a solution to the second order version of Palais problem. We also show that $\Ext^2(\ell_1, \K)\neq 0$ in ... More Homological dimensions of Banach spacesAug 18 2019The purpose of this paper is to lay the foundations for the study of the problem of when $\Ext^n(X, Y)=0$ in Banach/quasi-Banach spaces. We provide a number of examples of couples $X,Y$ so that $\Ext^n(X,Y)$ is (or is not ) $0$, including the first example ... More Riesz means in Hardy spaces on Dirichlet groupsAug 18 2019Given a frequency $\lambda=(\lambda_n)$, we study when almost all vertical limits of a $\mathcal{H}_1$-Dirichlet series $\sum a_n e^{-\lambda_ns}$ are Riesz-summable almost everywhere on the imaginary axis. Equivalently, this means to investigate almost ... More Ultraholomorphic extension theorems in the mixed settingAug 16 2019The aim of this work is to generalize the ultraholomorphic extension theorems from V. Thilliez in the weight sequence setting and from the authors in the weight function setting (of Roumieu type) to a mixed framework. Such mixed results have already been ... More A Theorem of Roe and Strichartz on homogeneous treesAug 16 2019In 1980, J. Roe proved that if $\{f_{k}\}_{k\in\mathbb{Z}}$ is doubly infinite sequence of functions in $\mathbb{R}$ which is uniformly bounded and satisfies $(df_{k}/dx)=f_{k+1}$ for all $k\in\mathbb{Z}$ then $f_{0}(x)=a\sin(x+\theta)$ for some $a,\theta\in\mathbb{R}$. ... More Iterative Neural Networks with Bounded WeightsAug 16 2019A recent analysis of a model of iterative neural network in Hilbert spaces established fundamental properties of such networks, such as existence of the fixed points sets, convergence analysis, and Lipschitz continuity. Building on these results, we show ... More Iterative Neural Networks with Bounded WeightsAug 16 2019Aug 19 2019A recent analysis of a model of iterative neural network in Hilbert spaces established fundamental properties of such networks, such as existence of the fixed points sets, convergence analysis, and Lipschitz continuity. Building on these results, we show ... More Noncommutative partial convexity via $Γ$-convexityAug 16 2019Motivated by classical notions of partial convexity, biconvexity, and bilinear matrix inequalities, we investigate the theory of free sets that are defined by (low degree) noncommutative matrix polynomials with constrained terms. Given a tuple of symmetric ... More Higher Rank Numerical Ranges of Jordan-Like MatricesAug 15 2019We completely characterize the higher rank numerical range of the matrices of the form $J_n(\alpha)\oplus\beta I_m$, where $J_n(\alpha)$ is the $n\times n$ Jordan block with eigenvalue $\alpha$. Our characterization allows us to obtain concrete examples ... More Moments of the weighted Cantor measuresAug 14 2019Based on the seminal work of Hutchinson, we investigate properties of {\em $\alpha$-weighted Cantor measures} whose support is a fractal contained in the unit interval. Here, $\alpha$ is a vector of nonnegative weights summing to $1$, and the corresponding ... More Operator inequalities I. Models and ergodicityAug 14 2019We discuss when an operator, subject to an inequality in heridatary form, admits a unitarily equivalent functional model of Agler type in the reproducing kernel Hilbert space associated to the inequality. To the contrary to the previous work, the kernel ... More On Expansive MappingsAug 14 2019When finding an original proof to a known result describing expansive mappings on compact metric spaces as surjective isometries, we reveal that relaxing the condition of compactness to total boundedness preserves the isometry property and nearly so that ... More A Tauberian theorem for ideal statistical convergenceAug 13 2019Given an ideal $\mathcal{I}$ on the positive integers, a real sequence $(x_n)$ is said to be $\mathcal{I}$-statistically convergent to $\ell$ provided that $$ \textstyle \left\{n \in \mathbf{N}: \frac{1}{n}|\{k \le n: x_k \notin U\}| \ge \varepsilon\right\} ... More Time-changed Dirac-Fokker-Planck equations on the latticeAug 13 2019A time-changed discretization for the Dirac equation is proposed. More precisely, we consider a Dirac equation with discrete space and continuous time perturbed by a time-dependent diffusion term $\sigma^2Ht^{2H-1}$ that resembles to a latticizing version ... More Projecting onto Helson matrices in Schatten classesAug 13 2019A Helson matrix is an infinite matrix $A = (a_{m,n})_{m,n\geq1}$ such that the entry $a_{m,n}$ depends only on the product $mn$. We demonstrate that the orthogonal projection from the Hilbert--Schmidt class $\mathcal{S}_2$ onto the subspace of Hilbert--Schmidt ... More Quantitative combinatorial geometry for concave functionsAug 12 2019We prove several exact quantitative versions of Helly's and Tverberg's theorems, which guarantee that a finite family of convex sets in $R^d$ has a large intersection. Our results characterize conditions that are sufficient for the intersection of a family ... More Positivity Certificates via Integral RepresentationsAug 12 2019Complete monotonicity is a strong positivity property for real-valued functions on convex cones. It is certified by the kernel of the inverse Laplace transform. We study this for negative powers of hyperbolic polynomials. Here the certificate is the Riesz ... More Bisynchronous Games and Factorizable MapsAug 11 2019We introduce a new class of non-local games, and corresponding densities, which we call bisynchronous. Bisynchronous games are a subclass of synchronous games and exhibit many interesting symmetries when the algebra of the game is considered. We develop ... More Wavelet transforms associated with the Index Whittaker transformAug 10 2019Aug 16 2019In this paper, we exploit the theory of convolution of index Whittaker transform for study of continuous and discrete Index Whittaker wavelet transform and discuss some of its basic properties. Certain boundedness, Plancherel as well as reconstruction ... More The angle along a curve and range-kernel complementarityAug 09 2019In this paper, we define the angle of a bounded linear operator $A$ along an unbounded path emanating from the origin and use it to characterize range-kernel complementarity. In particular we show that if $0$ faces the unbounded component of the resolvent ... More On convergent sequences in dual groupsAug 09 2019We provide some characterizations of precompact abelian groups $G$ whose dual group $G_p^\wedge$ endowed with the pointwise convergence topology on elements of $G$ contains a nontrivial convergent sequence. In the special case of precompact abelian \emph{torsion} ... More Large number of bubble solutions for a perturbed fractional Laplacian equationAug 09 2019This paper deals with the following nonlinear perturbed fractional Laplacian equation $$(-\Delta)^s u = K(|y'|,y'')u^{\frac{N+2s}{N-2s}\pm\epsilon},\,\,u>0,\,\,u\in D^{1,s}(\mathbb{R}^N),$$ where $0<s<1, N\geq 4,$ $(y',y'')\in \mathbb{R}^2\times \mathbb{R}^{N-2},$ ... More Embeddings of homogeneous Sobolev spaces on the entire spaceAug 09 2019We completely characterize the validity of the inequality $\|u\|_{Y(\mathbb{R}^n)}\leq C \|\nabla^m u\|_{X(\mathbb{R}^n)}$, where $X$ and $Y$ are rearrangement-invariant spaces, by reducing it to a considerably simpler one-dimensional inequality. Furthermore, ... More On Function Spaces with Mixed Norms --- A SurveyAug 09 2019The targets of this article are threefold. The first one is to give a survey on the recent developments of function spaces with mixed norms, including mixed Lebesgue spaces, iterated weak Lebesgue spaces, weak mixed-norm Lebesgue spaces and mixed Morrey ... More A generalization of order convergenceAug 08 2019Let $E$ be a sublattice of a vector lattice $F$. $\left( x_\alpha \right)\subseteq E$ is said to be $ F $-order convergent to a vector $ x $ (in symbols $ x_\alpha \xrightarrow{Fo} x $), whenever there exists another net $ \left(y_\alpha\right) $ in $F ... More Unbounded $σ$-order-to-norm continuous and $un$-continuous operatorsAug 08 2019An operator $T $ from a vector lattice $E$ into a normed lattice $F$ is called unbounded $\sigma$-order-to-norm continuous whenever $x_{n}\xrightarrow{uo}0$ implies $\| Tx_{n}\|\rightarrow 0$, for each sequence $(x_{n})_n\subseteq E$. For a net $(x_{\alpha})_{\alpha}\subseteq ... More Balian-Low type theorems on homogeneous groupsAug 08 2019We prove strict necessary density conditions for coherent frames and Riesz sequences on homogeneous groups. Let $N$ be a connected, simply connected nilpotent Lie group with a dilation structure (a homogeneous group) and let $(\pi, \mathcal{H}_{\pi})$ ... More Two remarks on the interpolation spaceAug 08 2019Dans ce travail, on montre que $(M(\mathbb{T}),c_0(\mathbb{Z}))_\theta = (L^1,c_0(\mathbb{Z}))_\theta$, $0<\theta <1$. Dans la suite on montre pour le couple d'interpolation $(C_0,C_1)$ trouv\'e par Garling-Smith qu'il existe un isomorphisme $U_\theta: ... More Two remarks on the interpolation spaceAug 08 2019Aug 14 2019Dans ce travail, on montre que $(M(\mathbb{T}),c_0(\mathbb{Z}))_\theta = (L^1,c_0(\mathbb{Z}))_\theta$, $0<\theta <1$. Dans la suite on montre pour le couple d'interpolation $(C_0,C_1)$ trouv\'e par Garling-Smith qu'il existe un isomorphisme $U_\theta: ... More Wall-to-wall optimal transportAug 08 2019Gradient ascent methods are developed to compute incompressible flows that maximize heat transport between two isothermal no-slip parallel walls. Parameterizing the magnitude of velocity fields by a P\'eclet number $\text{Pe}$ proportional to their root-mean-square ... More Wall-to-wall optimal transport in two dimensionsAug 08 2019Aug 20 2019Gradient ascent methods are developed to compute incompressible flows that maximize heat transport between two isothermal no-slip parallel walls. Parameterizing the magnitude of velocity fields by a P\'eclet number $\text{Pe}$ proportional to their root-mean-square ... More Biangular Gabor frames and Zauner's conjectureAug 07 2019Two decades ago, Zauner conjectured that for every dimension $d$, there exists an equiangular tight frame consisting of $d^2$ vectors in $\mathbb{C}^d$. Most progress to date explicitly constructs the promised frame in various dimensions, and it now appears ... More Sobolev type spaces associated with the Poly-axially operatorAug 07 2019In this paper n-dimensional Sobolev type spaces $ E_{\alpha}^{s,p}(\R^n_+)$ $(\alpha\in \R^n,\;\;\alpha_1> -\frac{1}{2},...,\alpha_n>-\frac{1}{2}, s\in \R, p\in [1,+\infty])$ are defined on $\R^n_+$ by using Fourier-Bessel transform. Some properties including ... More Spectrum is rational in dimension oneAug 07 2019A bounded measurable set $\Omega\subset{\mathbb R}^d$ is called a spectral set if it admits some exponential orthonormal basis $\{e^{2\pi i \langle\lambda,x\rangle}: \lambda\in\Lambda\}$ for $L^2(\Omega)$. In this paper, we show that in dimension one ... More Two Applications of Boolean Valued AnalysisAug 07 2019The paper contains two main results that are obtained by Boolean valued analysis. The first asserts that a universally complete vector lattice without locally one-dimensional bands can be decomposed into a direct sum of two vector sublattices that are ... More Open embeddings and pseudoflat epimorphismsAug 06 2019We characterize open embeddings of Stein spaces and of $C^\infty$-manifolds in terms of certain flatness-type conditions on the respective homomorphisms of function algebras. Plurisubharmonic Noncommutative Rational FunctionsAug 05 2019A noncommutative (nc) function in $x_1,\dots,x_g,x_1^*,\dots,x_g$ is called plurisubharmonic (plush) if its nc complex Hessian takes only positive semidefinite values on an nc neighborhood of 0. The main result of this paper shows that an nc rational ... More Factorizations of Schur functionsAug 05 2019The Schur class, denoted by $\mathcal{S}(\mathbb{D})$, is the set of all functions analytic and bounded by one in modulus in the open unit disc $\mathbb{D}$ in the complex plane $\mathbb{C}$, that is \[ \mathcal{S}(\mathbb{D}) = \{\varphi \in H^\infty(\mathbb{D}): ... Moremath.FAmath.CVmath.OAmath.OC32A10, 32A70, 47A48, 47A13, 46E15, 93B15, 15.40, 15A23, 93C35,
32A38, 30H05, 47N70, 93B28, 94A12 Symmetric shift-invariant subspaces and harmonic mapsAug 05 2019The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an important class ... More